Leonardo's father Guilielmo (William) was nicknamed Bonacci ('good natured' or 'simple'). Leonardo was posthumously given the nickname Fibonacci (for filius Bonacci, son of Bonacci). William directed a trading post (by some accounts he was the consul for Pisa) in Bugia, North Africa (now Bejaia[?], Algeria), and as a young boy Leonardo traveled there to help him. There he learnt from the Arabs the Indian numeral system.

Perceiving the superiority of these so-called Arabic numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time, returning around 1200. In 1202, at age 27, he published what he had learned in Liber Abaci, or Book of Calculation. This book showed the practical importance of the new number system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interests, money-changing, and numerous other applications. The book was enthusiastically received throughout educated Europe and had a profound impact on European thought.

Leonardo became a guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, under his alternative name of Leonardo Bigollo, by granting him a salary.